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baconossifiedMechanics

Oct 29, 2013 (3 years and 11 months ago)

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Phenomena and Problems in

Liquid Crystal Elastomers


Mark Warner, Cavendish Cambridge.

Classical Rubber

Locally a polymeric
liquid



mobile

Make more complex, keep locally fluid



More complex solids

Nematic fluid

cool

Nematic polymers have shape
anisotropy

Crosslink:

elastomers respond to
molecular shape change

monodomain

1

l

crosslink

block of rubber

Nematic Rubber

anisotropic
chains

initial

shape

current

shape

Change shape with
d
T

Tajbakhsh and Terentjev

Cavendish Laboratory

Roughly 300% strains.

Temperature changed by hot air blower.

Monodomain elastomer.

Close to real
-
time movement.

2

6

3.5

1

1.5

2

2.5

3

20

40

60

80

100

120

Temperature ( C)

Strain

L/L
0

Cross
-
section

~2mm
2


Load=15g

Load=10g

Load=5g

No Load

Smectic A

cool

Smectic
liquids


Nematic fluid with layered positional order.

Layer modulus 10
7

N/m
2
.

(DJ Cleaver
et al
, Sheffield)

n

k

Smectic C

2
-
D elastomer


layers so strong

(b) 90ºC (heating)

q
E

(a) 25ºC (heating)

L
E

(c) 130ºC

L
E

q
E

(Hiraoka and Finkelmann, 2005)

layers

k

n

P

Spontaneous
shears

of smectic sheet

(also possible with slab)

Reduce order by
bending

some rods


-

Photo alternative to thermal disruption of order.

Absorb photon into dye molecule

trans

isomer

cis

isomer

Azo benzene

(straight)

(bent)

Recovery

thermal or stimulated

Optical strains.

Thermal

Optical

Can be very fast.

Bend.

Polydomain response.

Birubber strip, H Finkelmann, Freiburg.

Non
-
uniform response

Nematic elastomer + green dye guest; laser pulse.



Dye photoisomerises

top has lower nematic order


differential

photo
-
contraction???

Green laser pulse

Palffy
-
Muhoray

* Curvature of photo
-
beams very rich (2 neutral planes)

* Optically write structures in films

Most peculiar dynamics


why does it continue curling after eclipsing itself?!

What should the photo
-
stationary shape be?

Photo
-
bending of sheets
(Ikeda, Nature, 2003)

E

Uncurling in the absence of UV.

(in light


stimulated decay)

Responsive surfaces and thin films

light beam
localised

strains

photo
-
rubber

Elongation on illumination

Rotate order rather than change magnitude

Stretch transverse to
director



Body accommodates
rotating chain distribution.



Need shear & stretch.



Entropy, energy constant.

thereafter hard.

inscribed

Minimised by (Olmsted):

Stretch transverse to
director

stretch

force/area

hard

Response by rotation pervades
all LC elastomer mechanics

E

45
o

Photo
-
bend also for
polydomains



depends on light polarisation

k

E

Light incident

Curl direction

light polarisation

(heat a minor effect?)

Polydomain photo
-
elastomer

(thin)

Incident light

Local molecular mobility


Domains suffer director
rotation away from
E



large change in natural shape

(MW & DC, PRL 06)

E

Photo contraction
l

along
E

non
-
monotonic

with intensity
I

recovered
l
,
all domains
isotropic

director
rotation
gives strain

back rotation starts

order parameter collapses

(“bleaching”) in back
-
rotated domains

back rotation complete

NMR? Mechanics?

Unpolarised light?

SmC* ferro electric


Spontaneous
shear

L

~ 0.4

Actuation based on shear.

Ferro
-
electric films respond to:



stress/strain



electric field



light



heat

k

n

c

p

q

L

Slab geometry for film

Apply shear
-
2
L

Reverse polarisation

Film bistable??

Cholesterics


helically twisted nematics:

Elastomers:

Separate left from right handed molecules.

Change colour on stretching.

Lase when pumped


lasing colour changes with stretch . . .

(tuneable laser from an elastic photonic band solid)

Deformations in practice (Quasi
-
convexification)

Stripes

Macroscopic extension

Kundler & Finkelmann

(crossed polars)

Replace gross deformations by microstructure of (soft) strains with
lower energy which satisfies constraints in gross sense.

Practical geometry


put stripes in where needed for lowest energy:

Conti
et al
(1/4 of strip)

(soft)

Zubarev, Finkelmann
et al

Terentjev
et al

(Depends on strip aspect ratio.)

Q
0

initially (and finally)

z

q
0

Jump away from ; global order
S < 0

z

n

~Q
0

q

Collapse of local order
Q
;
global order less negative

Jump back toward

z

n

Q
~0

q~q
0

Detect by NMR?

Local order
Q
0

rotated away from
E
; global
S
<0

Local and global order
= 0

Mahadevan
et al
(Phys. Rev. Letts., 2004)


Light intensity
I
(
x
)

falls with
x

(absorption length
d

)

Contraction decreases with
x

Bending (curling) of beam or sheet

thickness

rad. curvature

w>d
: thick

w<d
: thin film


Balance torques


get 2 neutral planes at depths
x
n

Curvature (
1/
R
)
non
-
monotonic

in
d/w

(absorption length/thickness)

Optimal
d

~
w
/3

“thick”

“thin”

(more examples)